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%I #28 Nov 17 2024 07:27:00
%S 1,2,4,16,134
%N Write the English name of a(n); sum the ranks of its letters in the alphabet; divide the sum by a(n); the result is an integer.
%C Is a(5) = 134 the last such term?
%C Indices of zeros in A226911; and conjectured finite, full based on an observation there. - _Michael S. Branicky_, Apr 07 2023
%C If a(6) exists, it is > 10^7. - _Robert G. Wilson v_, Apr 22 2023
%C There are no more terms because for any number k > 10^6, the sum of the ranks of the letters in the English name of k will be far less than k. - _Erich Friedman_, Nov 13 2024
%e a(1) = 1 = ONE and O+N+E = 34 and 34/1 = 34;
%e a(2) = 2 = TWO and T+W+O = 58 and 58/2 = 29;
%e a(3) = 4 = FOUR and F+O+U+R = 60 and 60/4 = 15;
%e a(4) = 16 = SIXTEEN and S+I+X+T+E+E+N = 96 and 96/16 = 6; etc.
%t Position[Array[Mod[Total@ Flatten[ToCharacterCode[#] - 96 & /@ Characters@ StringDelete[IntegerName[#], Except@ LetterCharacter]], #] &, 10^4] , 0][[All, 1]] (* _Michael De Vlieger_, Apr 07 2023 *)
%Y Cf. A092320, A126259, A073327, A226911.
%K base,nonn,fini,full,word,changed
%O 1,2
%A _Eric Angelini_ and Mensanator, Apr 07 2023